{"title":"Stability of an Advective Flow in a Horizontal Fluid Layer Heat-Insulated from Below with Rigid Boundaries","authors":"K. G. Shvarts, Yu. A. Shvarts","doi":"10.1134/S0015462822080055","DOIUrl":null,"url":null,"abstract":"<div><div><h3>\n <b>Abstract</b>—</h3><p>In this paper, we study the stability of an advective flow in a flat horizontal layer of an incompressible fluid with rigid boundaries. A linear temperature distribution is set on the upper boundary of the layer while the lower boundary is thermally insulated. The plane-parallel flow due to the action of horizontal convection is described analytically as an exact solution of the Navier–Stokes equations in the Boussinesq approximation. In the linear theory, the stability of an advective flow to normal perturbations is studied at various values of the Prandtl number. The most dangerous modes are determined, and neutral curves are plotted. In the nonlinear formulation of the problem, the structure of finite-amplitude perturbations in the supercritical region near the minima of the neutral curves is studied.</p></div></div>","PeriodicalId":560,"journal":{"name":"Fluid Dynamics","volume":"57 8","pages":"973 - 981"},"PeriodicalIF":0.6000,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fluid Dynamics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0015462822080055","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract—
In this paper, we study the stability of an advective flow in a flat horizontal layer of an incompressible fluid with rigid boundaries. A linear temperature distribution is set on the upper boundary of the layer while the lower boundary is thermally insulated. The plane-parallel flow due to the action of horizontal convection is described analytically as an exact solution of the Navier–Stokes equations in the Boussinesq approximation. In the linear theory, the stability of an advective flow to normal perturbations is studied at various values of the Prandtl number. The most dangerous modes are determined, and neutral curves are plotted. In the nonlinear formulation of the problem, the structure of finite-amplitude perturbations in the supercritical region near the minima of the neutral curves is studied.
期刊介绍：
Fluid Dynamics is an international peer reviewed journal that publishes theoretical, computational, and experimental research on aeromechanics, hydrodynamics, plasma dynamics, underground hydrodynamics, and biomechanics of continuous media. Special attention is given to new trends developing at the leading edge of science, such as theory and application of multi-phase flows, chemically reactive flows, liquid and gas flows in electromagnetic fields, new hydrodynamical methods of increasing oil output, new approaches to the description of turbulent flows, etc.
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